# Calendar: 1875-1876 Page 572

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568 GENERAL LITERATURE AND SCIENCE IL- tomttrD of Cluo or Cljrce SimtnSiaui Ii straight line be drawn parallel to one of the sides of triangle it shall cut the other two sides on those sides produced proportionally If the homologous sides of two similar triangles be parallel the lines joining corresponding vertices will meet in point If from point tangents QP QP" be drawn to para- bola the two triangles SPQ SQP' are similar Prove that the locus of the middle point of tbe portion of variable tangent to parabola intercepted between two fixed tangents is straight line The feet of the perpendiculars from the foci upon any tangent to an ellipse lie on the auxiliary circle The line joining the centre to the foot of the perpendicular from one of the foci on normal is parallel to the line joining the other focus to the point at which the normal is drawn Find the length of the perpendicular from the point hk upon the straight line Ax By the axes being rectangular Find the equation of the straight lines bisecting the angles between the straight lines Χ ב Χ "- and -L and prove that the area of the triangle they make with either axis is-- bf Two given straight lines are drawn through the vertex of parabola find the equation of the straight line joining the points in which they cut the curve If the straight lines be at right angles this line will cut the axis at distance from the vertex equal to the latus rectum Find the condition that the straight line x- should cr be tangent normal to the ellipse

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